How do I track time off, vacation, or sick days?

Create tasks for each category—vacation time, etc.—and add them to each of your existing projects for current clients.
With either option, users will then track time to those specific tasks.

If all of the time is captured within a single internal project, you can use its Project Analysis page to take a look at your data. If you have separate tasks for each of your projects, you can use a detailed time report to drill down and view exactly the user and task you want to see.